Question

Convert the decimals into their rational forms.
A. $0.\overline{4}$
B. $0.\overline{9}$
C. $16.\overline{78}$
D. $23.\overline{11}$
E. $19.\overline{51}$

Answer 1

$A.\mathrm{0.444..............}0.4+0.04+0.004+.........\infty \left(\frac{0.4}{1-0.1}\right)=\left(\frac{0.4}{0.9}\right)=\left(\frac{4}{9}\right)B.\mathrm{0.999............}=0.9+0.09+0.009+.........=\left(\frac{0.9}{1-0.1}\right)=\left(\frac{0.9}{0.9}\right)=1$